1. Field of the Invention
The present invention relates to the field of communications and, more particularly, to equalization for digital communication channels.
2. Description of the Related Art
Channel equalization plays a key role in digital communication systems. Typically, the physical channel introduces a distortion to the transmitted signal that can make it difficult to recover the original data. An equalizer can reduce, or ideally completely eliminate, the introduced intersymbol interference (ISI). Conventional equalization techniques rely on the transmission of a reference, or training, sequence that is known at the equalizer. This sequence allows adaptation of the equalizer parameters to minimize some cost function that measures the distance between the actual equalizer output and the desired reference signal. For instance, when the equalizer is implemented by means of a linear filter, the filter coefficients can be adapted using least mean squares analysis to minimize the expectation of the squared error. This type of equalization is referred to as supervised equalization.
When a training or reference sequence is not available at the receiver, blind equalization can be used. Without a reference sequence, the only knowledge about the transmitted sequence is limited to its probabilistic or statistical properties. Under this constraint, blind equalization typically minimizes a cost function that is able to indirectly extract the higher order statistics of the signal or the current level of ISI at the equalizer output. Typically, the cost function is minimized by means of a stochastic gradient algorithm. Examples of this kind of algorithm can include the Sato algorithm as disclosed in Y. Sato, “A method of self-recovering equalization for multilevel amplitude modulation,” IEEE Transactions on Communications, vol. COM-23, pp. 679-682 (1975); and the Godard algorithms as disclosed in D. N. Godard, “Self-recovering equalization and carrier tracking in two dimensional data communication systems,” IEEE Transactions on Communications, vol. 28, pp. 1867-1875, (November 1980).
One significant disadvantage of blind equalization techniques such as those noted herein is their need for a high number of data symbols to achieve convergence to a good solution. The high number of data symbols is necessary because the criterion for optimization is unable to exploit the high order statistics present in the data. Following an initial approximate equalization stage, which could be either supervised or blind, typically decision-directed equalization is employed. Decision-directed equalization utilizes discretized versions of the equalizer outputs as desired reference signal values. The discretization is typically done by approximating the current value of the output with the nearest value from the symbol alphabet called the symbol constellation.
Other techniques attempt to improve the convergence speed of conventional blind equalizers and utilize higher order statistics. For example, Renyi's entropy, as disclosed in I. Santamaria, et al., “A fast algorithm for adaptive blind equalization using Renyi's entropy,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, vol. III, Orlando, Fla., USA, 2002, pp. 2657-2660, has been used as a cost function for blind equalization of constant modulus signals. This approach is an application of information theoretic criteria to equalization and uses the Parzen window method (a nonparametric method) to estimate the underlying probability density function. A discussion of information theoretic criteria can be found in J. Principe, et al., “Learning from examples with information theoretic criteria,” Journal of VLSI Signal Processing, vol. 26, pp. 61-77, 2000. Although this method can provide acceptable results for some communication channels, Renyi's entropy does not produce acceptable results for ill-conditioned channels, or those having zeros at or very close to the unit circle. Further, this technique is sensitive to noise.
What is needed is an equalization technique that is applicable to any symbol constellation standard and which provides improved performance over existing equalization techniques.